I have litter trained my chi, it works great, neither of us have to go out in the cold when she has to potty.
Having said that, I don't use the clumping cat litter or the regular clay litter because my little girl will eat it and I can't imagine it wouldn't swell up in her tummy. May be it wouldn't cause any problems but I don't want to take the chance.
I use 'Yesterday's News' litter, it's the one that is made out of recycled news paper.
Jadzia uses it just fine and even if she eats a piece or two it's just paper. I'm always with her when she potties so I'm careful to watch that she doesn't eat any.
May be your little girl is jealous and doesn't want to go out in the cold LOL.